1. Field of the Invention
The present invention relates to a multi-beam scanning optical system and an image forming apparatus using the same. More particularly, the present invention is suitably implemented as an image forming apparatus, such as a laser beam printer and a digital copying machine, in which high-quality printing can be realized at high speed with a relatively simple construction.
2. Description of the Related Art
Hitherto, a scanning optical system used in an image forming apparatus, e.g., a laser beam printer and a digital copying machine, has such a construction that a light beam emitted from a light source is introduced to a deflecting unit through an entrance optical system, and the light beam deflected by the deflecting unit is focused by a scanning optical system into the form of a spot on a photoconductor drum surface, i.e., a surface to be scanned, thereby optically scanning the photoconductor drum surface with the light beam.
With recent improvements in performance and function of an image forming apparatus, a demand for operation at higher speed has increased more and more. One solution of meeting such a demand is to employ a plurality of light sources. For example, Japanese Patent Laid-Open No. 9-54263 proposes a multi-beam scanning optical system in which a light source is constituted as a multi-beam laser chip radiating, from one chip, a plurality of laser beams focused into spots lying on a line.
In that multi-beam scanning optical system, an optical means for beam synchronous detection (BD optical system) is usually disposed just upstream of a stage of writing an image signal for precise control of an image-write start position.
FIG. 18 is a sectional view (main scan section view) of principal part of a conventional multi-beam scanning optical system in the main scan direction. Referring to FIG. 18, numeral 51 denotes a light source unit comprising two light emitting portions (light sources) constituted by, e.g., semiconductor lasers. The two light emitting portions are separately arranged from each other in both the main scan direction and the sub-scan direction. Numeral 52 denotes an aperture diaphragm for shaping each of light beams emitted from the two light emitting portions into an optimum beam shape. Numeral 53 denotes a collimator lens for converting the light beams having passed the aperture diaphragm 52 into substantially parallel light beams. Numeral 54 denotes a cylindrical lens that has predetermined refracting power only in the sub-scan direction. The above-mentioned elements, such as the aperture diaphragm 52, the collimator lens 53 and the cylindrical lens 54, constitute respective components of an entrance optical system 62.
Numeral 55 denotes a deflecting unit (optical deflector) that is constituted by a rotating polygon mirror, for example, and is rotated at a constant speed in a direction of arrow PA, shown in FIG. 18, by a driving unit (not shown) such as a motor. Numeral 56 denotes a scanning optical system 56 that has the fxcex8 characteristic and comprises two first and second fxcex8 lenses. The scanning optical system 56 has the function of compensating an image plane tilt by holding, in a sub-scan section, a conjugate relationship between the vicinity of a deflecting surface 55a of the optical deflector 55 and the vicinity of a photoconductor drum surface 57 as a surface to be scanned.
Numeral 58 denotes a return mirror (referred to as a xe2x80x9cBD mirrorxe2x80x9d hereinafter) for reflecting, toward the side of a synchronous detection sensor 61 (described later), a plurality of light beams (referred to as xe2x80x9cBD light beamsxe2x80x9d hereinafter) used for detecting sync signals to adjust the timing of scan start positions on the photoconductor drum surface 57. Numeral 59 denotes a slit (referred to as a xe2x80x9cBD slitxe2x80x9d hereinafter) that is provided in a position optically equivalent to the photoconductor drum surface 57. Numeral 60 denotes a BD lens for making the BD mirror 58 and the synchronous detection sensor 61 located in a conjugate relationship and for compensating a plane tilt of the BD mirror 58. Numeral 61 denotes a photosensor (referred to as a xe2x80x9cBD sensorxe2x80x9d hereinafter) serving as the synchronous detection sensor 61. The above-mentioned elements, such as the return mirror 58, the BD slit 59, the BD lens 60 and the BD sensor 61, constitute respective components of an optical means for beam synchronous detection (BD optical system).
With the arrangement of FIG. 18, beam synchronous detection is performed for each of the BD light beams emitted from the two light emitting portions, and the timing of a scan start position in recording of an image on the photoconductor drum surface 57 is adjusted for each light beam emitted from the light emitting portion by using an output of the BD sensor 61.
In a multi-beam scanning optical system including a plurality of light emitting portions (light sources), however, if the relative positional relationship between respective light beams emitted from the plurality of light sources in the main scan direction is changed on a surface to be scanned with the progress of scan for various reasons, degradation of a printed image occurs. Also, in spite of that the relative positional relationship between the light emitting portions in the main scan direction is not changed during scan, degradation of a printed image also occurs if write start positions are shifted from each other between the light emitting portions.
Such a phenomenon is conceivably caused by a shift of focus position of the BD light beam on the plane of a BD slit (namely, the BD light beam is not properly focused because it is out of focus on the plane of the BD slit) and a shift of focus position of the scanning light beam on the surface to be scanned.
A shift of focus position of the BD light beam on the BD slit plane will be described below with reference to FIGS. 19 to 26. Note that, for the sake of clearer representation, the BD sensor that should be illustrated on the upper side in the figure is omitted from all of FIGS. 19 to 26. Also, marginal rays are omitted in FIGS. 20A, 23A, 25A and 26A.
FIG. 19A shows a state at the moment when two light beams (herein, a light beam A emitted from one light emitting portion and a light beam B emitted from the other light emitting portion) are focused just at one end (right end as viewed on the figure) of the BD slit in the main scan direction. The light beam A scanned from the left to the right in FIG. 19A does not enter the BD sensor until it reaches just the right end of the BD slit. Upon the light beam A reaching the right end of the BD slit, the BD sensor outputs a signal indicating the incidence of the light beam A. Similarly to the light beam A, the light beam B scanned from the left to the right does not enter the BD sensor until it reaches just the right end of the BD slit, and the BD sensor outputs a signal indicating the incidence of the light beam B upon reaching the right end of the BD slit. The timing of write start positions of the light beams A, B is adjusted by detecting the timed relationship between the two output signals from the BD sensor.
However, if the focus positions of the light beams A, B having passed the BD optical system are relatively shifted xcex4M, as shown in FIG. 20A, in the main scan section to the upstream side looking from the slit, i.e., to the side nearer to the deflecting unit, the following phenomenon occurs and the write start positions of the light beams A, B are shifted from each other. More specifically, at the timing at which the light beam A should be focused at the right end of the BD slit and should start entering the BD sensor unless the light beam A is not defocused, the light beam A already enters the surface of the BD sensor because of defocusing (namely, the defocused light beam A at the proper detection timing in this case is indicated by a broken line on the left side in FIG. 20A). The light beam A actually starts entering the BD sensor at the timing when it has reached a position indicated by a solid line on the left side in FIG. 20A (as represented by xe2x80x9cdefocused light beam A actually first detectedxe2x80x9d). Thus, the write start timing of the light beam A is advanced corresponding to a shift between the broken line and the solid line on the left side. Conversely, the light beam B should start entering the BD sensor at the timing when it has reached a position indicated by a broken line on the right side in FIG. 20A (as represented by xe2x80x9cdefocused light beam B at proper detecting timingxe2x80x9d), but it cannot enter the BD sensor at that timing because of defocusing. The light beam B is able to actually enter the BD sensor only after it has reached a position indicated by a solid line on the right side in FIG. 20A (as represented by xe2x80x9cdefocused light beam B actually first detectedxe2x80x9d). Thus, the write start timing of the light beam B is delayed corresponding to a shift between the broken line and the solid line on the right side. As a result, the relative write start positions of the light beams A, B are shifted depending on the distance between the two broken lines on the plane of the BD slit. A relative write start position shift xcex4Yb occurred on the surface to be scanned at that time is determined as follows.
A distance xcex4Ybxe2x80x2 between the two broken lines on the plane of the BD slit is determined based on a focus shift amount xcex4M measured looking from the slit plane and an angle difference xcex8b [rad] between incident angles of the two light beams when they have reached the right end of the slit. Then, the distance xcex4Ybxe2x80x2 can be approximately expressed by:
xcex4Ybxe2x80x2=xcex4Mxc3x97xcex8bxe2x80x83xe2x80x83(1) 
Herein, the angle difference xcex8b between incident angles of the two light beams is attributable to the fact that deflecting points of the light beams A, B are shifted from each other when they are deflected by the deflecting surface, and is caused due to the fact that the two light beams pass different areas of a lens unit for focusing the light beams, after being deflected by the deflecting surface, to the vicinity of the slit plane in the main scan section.
If the relative position shift xcex4Ybxe2x80x2 on the slit plane occurs between the light beams A and B as described above, an angle xcfx86 by which the deflecting unit (deflecting surface) is rotated during a period from the incidence of the light beam A upon the BD sensor to the time at which the light beam B starts entering the BD sensor is increased, as expressed by the following formula (2), in comparison with the case that the BD optical system is free from defocusing:
xcfx86=Arctan((xcex4Ybxe2x80x2/2)/Fb)xe2x80x83xe2x80x83(2) 
In the formula (2), Fb is the focal distance of the lens unit for focusing the light beams, after being deflected by the deflecting surface, to the vicinity of the slit plane in the main scan section, and it is usually greater than xcex4Ybxe2x80x2 on the order of two digits. Therefore, the formula (2) can be approximately expressed by:
xcfx86=0.5xc3x97xcex4Ybxe2x80x2/Fbxe2x80x83xe2x80x83(3) 
Because the scanning optical system has the fxcex8 characteristic, the relative write start position shift xcex4Yb on the surface to be scanned is given by the following formula (4) on an assumption that the focal distance of the scanning optical system is Ff:
xcex4Yb=2xc3x97Ffxcfx86=(Ff/Fb)xc3x97xcex4Ybxe2x80x2=(Ff/Fb)xc3x97(xcex4Mxc3x97xcex8b)xe2x80x83xe2x80x83(4) 
Thus, the write start position shift xcex4Yb is given by a value resulting from multiplying the relative position shift xcex4Ybxe2x80x2 on the BD slit plane by a lateral magnification ratio (Ff/Fb) between the synchronous detection optical system and the scanning optical system.
If the focus position is shifted from the slit plane in the synchronous detection optical system, a scanning line provided by the light beam A and a scanning line provided by the light beam B are shifted from each other, as described above, in the main scan direction by an amount of xcex4Yb expressed by the formula (4). On the other hand, if the focus position is shifted xcex4X to the side nearer to the deflecting unit looking from the surface to be scanned, as shown in FIG. 21, in spite of the synchronous detection optical system being free from defocusing, a point of intersection between the light beams A and B is shifted xcex4X to the side nearer to the deflecting unit. In that case, therefore, there occurs a relative position shift xcex4Yf between the light beams A and B in the main scan direction (such a phenomenon, including the above-mentioned write start position shift, is referred to as a xe2x80x9cdot position shiftxe2x80x9d hereinafter). The relative dot position shift xcex4Yf is determined as described below with reference to FIG. 21. Note that since the dot position shift occurs depending on defocusing of each image height in a scan area looking from the surface to be scanned, the dot position shift amount is generally not constant due to an effect of curvature of the image plane, etc.
FIGS. 21A and 21B show the positional relationship between two light beams (herein light beams A and B) at the moment when the light beams A and B are going to print images at the same height while they are defocused by a distance xcex4X toward the upstream side, i.e., the side nearer to the deflecting unit, looking from the surface to be scanned. In this case, because the focus position is shifted by the distance xcex4X, the focuses of the two light beams are aligned with each other at a position spaced by the distance xcex4X from the surface to be scanned. However, the surface to be scanned is in fact apart by the distance xcex4X from the aligned focus position toward the downstream side, and hence a relative position shift between the light beams A and B is approximately expressed by;
xcex4Yf=xcex4Xxc3x97xcex8fxe2x80x83xe2x80x83(5) 
where xcex8f [rad] represents an angle difference between incident angles of the light beams A and B upon the surface to be scanned when they reach a certain image height.
Accordingly, a dot position shift xcex4Y, taking into account both the focus shift xcex4Yb caused by the synchronous detection optical system and the focus shift xcex4Yf caused by the scanning optical system, is expressed by:
xcex4Y=xcex4Yfxe2x88x92xcex4Yb=xcex4Xxc3x97xcex8fxe2x88x92(Ff/Fb)xc3x97xcex4Mxc3x97xcex8bxe2x80x83xe2x80x83(6) 
The signs of xcex4Yf and xcex4Yb on the right side of the formula (6) differ from each other for the reason given below. When the light beam is defocused toward the upstream side due to the synchronous detection optical system, the write start position of a scanning line provided by the light beam A is shifted in a direction to locate ahead with respect to the write start position of a scanning line provided by the light beam B. On the other hand, When the light beam is defocused toward the upstream side due to the scanning optical system, the write start position of the light beam B is shifted in a direction to locate ahead with respect to the write start position of the light beam A.
Further, the incident angle differences xcex8f and xcex8b can be approximated as follows, assuming that d represents a position shift amount on the reflecting surface between the light beams A and B in the main scan direction when the reflecting surface is positioned in a face-to-face relation to the light sources:
xcex8b=d/Fbxe2x80x83xe2x80x83(7a) 
xcex8f=d/Ffxe2x80x83xe2x80x83(7b) 
Accordingly, the formula (6) can be modified to:
xcex4Y=[(Fb/Ff)xc3x97xcex4Xxe2x88x92(Ff/Fb)xc3x97xcex4M]xc3x97xcex8bxe2x80x83xe2x80x83(8a) 
or
xcex4Y=[xcex4Xxe2x88x92(Ff/Fb)2xc3x97xcex4M]xc3x97xcex8fxe2x80x83xe2x80x83(8b) 
Although the above description is made on the premise that there are two light sources, the discussion is similarly applied to the case in which there are three or more light sources in practice. A maximum shift amount xcex4Ytotal among dot position shifts xcex4Y between respective light emitting portions is given as follows, assuming that a maximum angle difference between the incident angles of the light beams upon the slit plane is xcex8max [rad]:
xcex4Ytotal=[(Fb/Ff)xc3x97xcex4Xxe2x88x92(Ff/Fb)xc3x97xcex4M]xc3x97xcex8maxxe2x80x83xe2x80x83(9) 
Hence, assuming that a maximum value among allowable dot position shifts xcex4Y between respective scanning lines is xcex4Ymax, the multi-beam scanning optical system requires to be arranged so that the focus shift amounts xcex4M and xcex4X satisfy the following formula (10):
|(Fb/Ff)xc3x97xcex4Xxe2x88x92(Ff/Fb)xc3x97xcex4M|xe2x89xa6xcex4Ymax/xcex8maxxe2x80x83xe2x80x83(10) 
Incidentally, when the multi-beam scanning optical system is arranged so as to satisfy the formula (10), the best spot position may be shifted from the position of the surface to be scanned in some cases. However, image quality is hardly affected so long as the focus position is within the allowable depth range.
Also, the maximum value xcex4Ymax of the dot position shift is preferably not larger than about a half the resolution in the sub-scan direction. If the maximum value xcex4Ymax exceeds such a level, adjacent horizontal lines would appear shifted from each other and a printed result would be very unsightly.
Given xcex4Ymax=10.5 xcexcm (corresponding to a half dot of 1200 dpi), xcex8max=0.3 [deg], Ff=140 mm, and Fb=70 mm,
for example, xcex4X is given by;
xcex4Xxe2x89xa64.0 mm
in the case of xcex4M=0, and xcex4M is given by;
xcex4Mxe2x89xa61.0 mm
in the case of xcex4X=0.
Although the above description is made of the case in which the focus position is shifted to the upstream side of the BD slit, the discussion is similarly applied to the case in which the focus position is shifted to the downstream side of the BD slit, as seen from FIGS. 22 to 26.
FIGS. 22A and 22B are explanatory views showing a reference state for explaining the positional relationship between two light beams when the focus position is shifted to the downstream side (i.e., the side away from the deflecting unit). FIGS. 23A and 23B are explanatory views showing the positional relationship between two light beams when the focus position is shifted to the downstream side (i.e., the side away from the deflecting unit) relative to the BD slit, and FIGS. 24A and 24B are explanatory views showing the positional relationship between two light beams when the focus position is shifted to the downstream side (i.e., the side away from the deflecting unit) relative to the surface to be scanned. FIGS. 25A and 25B are explanatory views showing the positional relationship between two light beams when the focus position is shifted to the upstream side (i.e., the side nearer to the deflecting unit) relative to the BD slit and the surface to be scanned, and FIGS. 26A and 26B are explanatory views showing the positional relationship between two light beams when the focus position is shifted to the downstream side (i.e., the side away from the deflecting unit) relative to the BD slit and the surface to be scanned.
Further, when the incident angles of the light beams upon the surface to be scanned are exactly the same, xcex8max=0 is resulted because the incident angles upon the BD slit are also all equal to each other from the formula (7). Accordingly, as seen from the formula (9), there occurs no dot position shift due to the focus position shift. However, such a condition is established only when the light emitting portions are arranged with no shift in the main scan direction, i.e., when the light emitting portions are arranged to lie on a line in the sub-scan direction, or only when a diaphragm or a conjugate point of a diaphragm is arranged on the deflecting surface so that principal rays of the light beams cross each other on the deflecting surface.
The former case gives rise to problems as follows. When the light emitting portions are arranged with no shift in the main scan direction, in particular, when a magnifying system is included in the sub-scan direction, the distance between the light emitting portions becomes usually too short on the order of several xcexcm to ten and odds xcexcm (the distance therebetween in an ordinary commercially available multi-laser is about 100 xcexcm). Therefore, crosstalk occurs and the light emitting portions generate light in different amounts. As a result, stable oscillation is no longer ensured and the useful life is shortened.
The latter case gives rise to problems as follows. When arranging a diaphragm on the deflecting surface, a desired condition can be obtained by causing the deflecting surface to provide in itself the function as a diaphragm without placing any member corresponding to a diaphragm at least in the main scan direction. With that arrangement, however, the width of a light beam is changed as deflecting scan proceeds, thus resulting in disadvantages that the spot diameter is changed and the amount of light is also changed. Further, using a relay optical system is known as a method for providing a conjugate point of a diaphragm on the deflecting surface. However, the method using a relay optical system is disadvantageous in that the number of necessary optical elements is increased and effectiveness in both space and cost is deteriorated.
Further, for a multi-beam scanning optical system including no BD slit in the BD optical system, an edge of the BD sensor eventually plays as the role of the BD slit. Therefore, the above discussion is similarly applied by replacing the right end of the BD slit with the left end of an effective area of the BD sensor and the plane of the BD slit with the light receiving surface of the BD sensor, respectively, in the above description.
In addition, while the scan direction is described above as directing from the left to the right, the above discussion is also similarly applied to the case in which the scan direction is reversed, except that the timing of deciding the write start position is changed from the right end of the illustrated BD slit to the left end of a not-shown BD slit on the right side.
Accordingly, it is an object of the present invention to provide a multi-beam scanning optical system and an image forming apparatus using the same, in which high-quality printing can be realized at high speed with a relatively simple construction.
According to one aspect of the present invention, there is provided a multi-beam scanning optical system comprising an entrance optical unit for introducing, to a deflecting unit, a plurality of light beams emitted from a light source unit having a plurality of light emitting portions arranged apart from each other at least in a main scan direction; a scanning optical unit for focusing the plurality of light beams deflected by the deflecting unit on a surface to be scanned; and a synchronous detection optical unit for converging, by a synchronous detection lens unit, parts of the plurality of light beams deflected by the deflecting unit on a plane of a slit, introducing the parts of the plurality of light beams to a synchronous detection sensor, and controlling timing of scan start positions on the surface to be scanned with respect to the plurality of light beams by using signals from the synchronous detection sensor, wherein, assuming that a focal distance of the scanning optical unit is Ff, a focal distance of the synchronous detection lens unit is Fb, a focus position shift amount of each light beam introduced to the synchronous detection sensor in a main scan section is xcex4M1 looking from the slit, a focus position shift amount of each image height is xcex4X looking from the surface to be scanned, an allowable dot position shift amount of each scanning line is xcex4Ymax, and a maximum angle difference between incident angles of the light beams upon the slit plane is xcex8max, Ffxe2x89xa0Fb holds and the following conditional formula is satisfied:
|(Fb/Ff)xc3x97xcex4Xxe2x88x92(Ff/Fb)xc3x97xcex4M1|xe2x89xa6xcex4Ymax/xcex8max 
In the above multi-beam scanning optical system, preferably, the allowable dot position shift amount of each scanning line is not larger than xc2xd of resolution in a sub-scan direction.
The above multi-beam scanning optical system preferably further comprises a compensating unit for shifting a focus position, in the main scan section, of each light beam introduced to the synchronous detection sensor in a direction of an optical axis of the synchronous detection optical unit relative to the slit.
The above multi-beam scanning optical system preferably includes a compensating unit for shifting a position of the slit or a unit including the slit in the direction of the optical axis of the synchronous detection optical unit.
In the above multi-beam scanning optical system, preferably, the synchronous detection lens unit is disposed in an optical path between the deflecting unit and the slit, and includes a compensating unit for shifting at least one lens of the synchronous detection lens unit in the direction of the optical axis of the synchronous detection optical unit.
In the above multi-beam scanning optical system, preferably, the synchronous detection lens unit comprises a single lens and is formed integrally with a part of optical elements constituting the entrance optical unit.
According to another aspect of the present invention, there is provided a multi-beam scanning optical system comprising an entrance optical unit for introducing, to a deflecting unit, a plurality of light beams emitted from a light source unit having a plurality of light emitting portions arranged apart from each other at least in a main scan direction; a scanning optical unit for focusing the plurality of light beams deflected by the deflecting unit on a surface to be scanned; and a synchronous detection optical unit for converging, by a synchronous detection lens unit, parts of the plurality of light beams deflected by the deflecting unit on a plane of a slit, introducing the parts of the plurality of light beams to a synchronous detection sensor, and controlling timing of scan start positions on the surface to be scanned with respect to the plurality of light beams by using signals from the synchronous detection sensor, wherein the multi-beam scanning optical system further comprises a compensating unit for compensating a dot position shift of each scanning line on the surface to be scanned, the dot position shift being caused by the fact that, assuming that a focal distance of the scanning optical unit is Ff, a focal distance of the synchronous detection lens unit is Fb, a focus position shift amount of each light beam introduced to the synchronous detection sensor in a main scan section is xcex4M1 looking from the slit, and a focus position shift amount of each image height is xcex4X looking from the surface to be scanned, Ffxe2x89xa0Fb holds and |(Fb/Ff)xc3x97xcex4Xxe2x88x92(Ff/Fb)xc3x97xcex4M1| has a certain value.
In the above multi-beam scanning optical system, preferably, a dot position shift amount of each scanning line on the surface to be scanned is not larger than xc2xd of resolution in a sub-scan direction.
The above multi-beam scanning optical system preferably further comprises a compensating unit for shifting a focus position, in the main scan section, of each light beam introduced to the synchronous detection sensor in a direction of an optical axis of the synchronous detection optical unit relative to the slit.
The above multi-beam scanning optical system preferably includes a compensating unit for shifting a position of the slit or a unit including the slit in the direction of the optical axis of the synchronous detection optical unit.
In the above multi-beam scanning optical system, preferably, the synchronous detection lens unit is disposed in an optical path between the deflecting unit and the slit, and includes a compensating unit for shifting at least one lens of the synchronous detection lens unit in the direction of the optical axis of the synchronous detection optical unit.
In the above multi-beam scanning optical system, preferably, the plurality of light emitting portions are arranged apart from each other in the sub-scan direction.
In the above multi-beam scanning optical system, preferably, the slit or a unit including the slit is inclined in the sub-scan direction depending on the dot position shift amount of each scanning line on the surface to be scanned.
The above multi-beam scanning optical system preferably further comprises an angle adjusting unit rotating the slit or a unit including the slit about the optical axis of the synchronous detection optical unit depending on the dot position shift amount of each scanning line on the surface to be scanned.
According to still another aspect of the present invention, there is provided a multi-beam scanning optical system comprising an entrance optical unit for introducing, to a deflecting unit, a plurality of light beams emitted from a light source unit having a plurality of light emitting portions arranged apart from each other at least in a main scan direction; a scanning optical unit for focusing the plurality of light beams deflected by the deflecting unit on a surface to be scanned; and a synchronous detection optical unit for introducing, by a synchronous detection lens unit, parts of the plurality of light beams deflected by the deflecting unit to a synchronous detection sensor and controlling timing of scan start positions on the surface to be scanned with respect to the plurality of light beams by using signals from the synchronous detection sensor, wherein, assuming that a focal distance of the scanning optical unit is Ff, a focal distance of the synchronous detection lens unit is Fb, a focus position shift amount of each light beam introduced to the synchronous detection sensor in a main scan section is xcex4M2 looking from a light receiving surface of the synchronous detection sensor, a focus position shift amount of each image height is xcex4X looking from the surface to be scanned, an allowable dot position shift amount of each scanning line is xcex4Ymax, and a maximum angle difference between incident angles of the light beams upon the light receiving surface of the synchronous detection sensor is xcex8max, Ffxe2x89xa0Fb holds and the following conditional formula is satisfied:
|(Fb/Ff)xc3x97Xxe2x88x92(Ff/Fb)xc3x97xcex4M2|xe2x89xa6xcex4Ymax/xcex8max 
In the above multi-beam scanning optical system, preferably, the allowable dot position shift amount of each scanning line is not larger than xc2xd of resolution in a subscan direction.
The above multi-beam scanning optical system preferably further comprises a compensating unit for shifting a focus position, in the main scan section, of each light beam introduced to the synchronous detection sensor in a direction of an optical axis of the synchronous detection optical unit relative to the light receiving surface of the synchronous detection sensor.
In the above multi-beam scanning optical system, preferably, the multi-beam scanning optical system includes a compensating unit for shifting a position of the synchronous detection sensor or a unit including the synchronous detection sensor in the direction of the optical axis of the synchronous detection optical unit.
In the above multi-beam scanning optical system, preferably, the synchronous detection lens unit is disposed in an optical path between the deflecting unit and the synchronous detection sensor, and includes a compensating unit for shifting at least one lens of the synchronous detection lens unit in the direction of the optical axis of the synchronous detection optical unit.
In the above multi-beam scanning optical system, preferably, the synchronous detection lens unit comprises a single lens and is formed integrally with a part of optical elements constituting the entrance optical unit.
According to still another aspect of the present invention, there is provided a multi-beam scanning optical system comprising an entrance optical unit for introducing, to a deflecting unit, a plurality of light beams emitted from a light source unit having a plurality of light emitting portions arranged apart from each other at least in a main scan direction; a scanning optical unit for focusing the plurality of light beams deflected by the deflecting unit on a surface to be scanned; and a synchronous detection optical unit for introducing, by a synchronous detection lens unit, parts of the plurality of light beams deflected by the deflecting unit to a synchronous detection sensor and controlling timing of scan start positions on the surface to be scanned with respect to the plurality of light beams by using signals from the synchronous detection sensor, wherein the multi-beam scanning optical system further comprises a compensating unit for compensating a dot position shift of each scanning line on the surface to be scanned, the dot position shift being caused by the fact that, assuming that a focal distance of the scanning optical unit is Ff, a focal distance of the synchronous detection lens unit is Fb, a focus position shift amount of each light beam introduced to the synchronous detection sensor in a main scan section is xcex4M2 looking from a light receiving surface of the synchronous detection sensor, and a focus position shift amount of each image height is xcex4X looking from the surface to be scanned, Ffxe2x89xa0Fb holds and |(Fb/Ff)xc3x97xcex4Xxe2x88x92(Ff/Fb)xc3x97xcex4M2| has a certain value.
In the above multi-beam scanning optical system, preferably, a dot position shift amount of each scanning line on the surface to be scanned is not larger than xc2xd of resolution in a sub-scan direction.
In the above multi-beam scanning optical system, preferably, the plurality of light emitting portions are arranged apart from each other in the sub-scan direction.
The above multi-beam scanning optical system, preferably further comprises a compensating unit for shifting a focus position, in the main scan section, of each light beam introduced to the synchronous detection sensor in a direction of an optical axis of the synchronous detection optical unit relative to the light receiving surface of the synchronous detection sensor.
In the above multi-beam scanning optical system, preferably, the multi-beam scanning optical system includes a compensating unit for shifting a position of the synchronous detection sensor or a unit including the synchronous detection sensor in the direction of the optical axis of the synchronous detection optical unit.
In the above multi-beam scanning optical system, preferably, the synchronous detection lens unit is disposed in an optical path between the deflecting unit and the synchronous detection sensor, and includes a compensating unit for shifting at least one lens of the synchronous detection lens unit in the direction of the optical axis of the synchronous detection optical unit.
According to still another aspect of the present invention, there is provided a multi-beam scanning optical system comprising an entrance optical unit for introducing, to a deflecting unit, a plurality of light beams emitted from a light source unit having a plurality of light emitting portions arranged apart from each other at least in a main scan direction; a scanning optical unit for focusing the plurality of light beams deflected by the deflecting unit on a surface to be scanned; and a synchronous detection optical unit for converging, by a synchronous detection lens unit, parts of the plurality of light beams deflected by the deflecting unit on a plane of a slit, introducing the parts of the plurality of light beams to a synchronous detection sensor, and controlling timing of scan start positions on the surface to be scanned with respect to the plurality of light beams by using signals from the synchronous detection sensor, wherein an amount of dot position shift of each scanning line on the surface to be scanned is not larger than xc2xd of resolution in a sub-scan direction, the dot position shift being caused by the fact that, assuming that a focal distance of the scanning optical unit is Ff, a focal distance of the synchronous detection lens unit is Fb, a focus position shift amount of each light beam introduced to the synchronous detection sensor in a main scan section is xcex4M1 looking from the slit, and a focus position shift amount of each image height is xcex4X looking from the surface to be scanned, Ffxe2x89xa0Fb holds and |(Fb/Ff)xc3x97xcex4Xxe2x88x92(Ff/Fb)xc3x97xcex4M1| has a certain value.
According to still another aspect of the present invention, there is provided a multi-beam scanning optical system comprising an entrance optical unit for introducing, to a deflecting unit, a plurality of light beams emitted from light source unit having a plurality of light emitting portions arranged apart from each other at least in a main scan direction; a scanning optical unit for focusing the plurality of light beams deflected by the deflecting unit on a surface to be scanned; and a synchronous detection optical unit for introducing, by a synchronous detection lens unit, parts of the plurality of light beams deflected by the deflecting unit to a synchronous detection sensor and controlling timing of scan start positions on the surface to be scanned with respect to the plurality of light beams by using signals from the synchronous detection sensor, wherein an amount of dot position shift of each scanning line on the surface to be scanned is not larger than xc2xd of resolution in a sub-scan direction, the dot position shift being caused by the fact that, assuming that a focal distance of the scanning optical unit is Ff, a focal distance of the synchronous detection lens unit is Fb, a focus position shift amount of each light beam introduced to the synchronous detection sensor in a main scan section is xcex4M2 looking from a light receiving surface of the synchronous detection sensor, and a focus position shift amount of each image height is xcex4X looking from the surface to be scanned, Ffxe2x89xa0Fb holds and |(Fb/Ff)xc3x97xcex4Xxe2x88x92(Ff/Fb)xc3x97xcex4M2| has a certain value.
According to still another aspect of the present invention, there is provided an image forming apparatus comprising one of the multi-beam scanning optical systems set forth above; a photoconductor arranged on a surface to be scanned; a developing unit for developing, into a toner image, an electrostatic latent image formed on the photoconductor by light beams scanned by the multi-beam scanning optical system; a transfer unit for transferring the developed toner image onto a material to which the toner image is to be transferred; and a fusing unit for fusing the transferred toner image onto the material to which the toner image is to be transferred.
According to still another aspect of the present invention, there is provided an image forming apparatus comprising one of the multi-beam scanning optical systems set forth above; and a printer controller for converting code data inputted from an external device into an image signal and applying the image signal to the beam scanning optical system.
Further objects, features and advantages of the present invention will become apparent from the following description of the preferred embodiments with reference to the attached drawings.